Subgroups — C₂²×C₆₁×#576 #29566517

Order 15616.

11462 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#576	C₂	1	48	yes	maximal, direct product factor
3	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	6	yes	maximal, complemented
4	C₂²×#135×C₆₁	C₂	1	3	yes	maximal, complemented
5	C₂³×D₈×C₆₁	C₂	1	3	yes	maximal, complemented
6	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(5,𝔽₂)×C₆₁	—	2	24	no	—
8	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	48	yes	complemented
9	C₂²×#41×C₆₁	—	2	2	no	—
10	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₆₁	C₂²	1	6	yes	complemented
12	C₂³×D₄×C₆₁	—	2	6	no	—
13	C₂³×D₄×C₆₁	C₂²	1	6	yes	complemented
14	C₆₁×#576	C₂²	1	256	yes	direct product factor
15	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	144	yes	complemented
16	C₂×#135×C₆₁	C₂²	1	72	yes	complemented
17	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×SD₁₆×C₆₁	C₂²	1	6	yes	complemented
19	C₂²×D₈×C₆₁	C₂²	1	3	yes	complemented
20	C₂²×D₈×C₆₁	C₂²	1	6	yes	complemented
21	C₂²×D₈×C₆₁	C₂²	1	72	yes	complemented
22	C₂×#131×C₆₁	C₂²	1	24	yes	complemented
23	C₂²×M₁₆×C₆₁	C₂²	1	3	yes	complemented
24	C₂³×C₈×C₆₁	C₂²	1	3	yes	complemented
25	C₂⁵×C₆₁	—	2	6	no	—
26	H(5,𝔽₂)×C₆₁	—	2	192	no	—
27	H(5,𝔽₂)×C₆₁	C₂³	1	128	yes	complemented
28	C₂×#41×C₆₁	—	2	48	no	—
29	C₂×#41×C₆₁	—	2	36	no	—
30	C₂×#41×C₆₁	D₄	1	12	yes	—
31	C₂×#41×C₆₁	C₂³	1	12	yes	—
32	C₂×#41×C₆₁	C₂³	1	72	yes	complemented
33	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
34	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
35	C₂²×D₄×C₆₁	—	2	6	no	—
36	C₂²×D₄×C₆₁	—	2	144	no	—
37	C₂²×D₄×C₆₁	—	2	6	no	—
38	C₂²×D₄×C₆₁	—	2	36	no	—
39	C₂²×D₄×C₆₁	D₄	1	3	yes	—
40	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
41	C₂²×D₄×C₆₁	C₂³	1	72	yes	complemented
42	C₂³×C₄×C₆₁	—	2	6	no	—
43	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
44	AGL(1,ℤ/8)×C₆₁	C₂³	1	384	yes	complemented
45	#135×C₆₁	C₂³	1	192	yes	complemented
46	C₂×Q₁₆×C₆₁	C₂³	1	12	yes	complemented
47	C₂×SD₁₆×C₆₁	C₂³	1	72	yes	complemented
48	C₂×D₈×C₆₁	C₂³	1	36	yes	complemented
49	C₂×D₈×C₆₁	C₂³	1	72	yes	complemented
50	C₂×D₈×C₆₁	C₂³	1	192	yes	complemented
51	#131×C₆₁	C₂³	1	64	yes	complemented
52	C₂×M₁₆×C₆₁	C₂³	1	36	yes	complemented
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
55	C₂²×C₈×C₆₁	C₂³	1	36	yes	complemented
56	C₂⁴×C₆₁	—	2	6	no	—
57	C₂⁴×C₆₁	—	2	72	no	—
58	C₂⁴×C₆₁	—	8	24	no	—
59	C₂⁴×C₆₁	C₂×D₄	1	3	yes	—
60	#41×C₆₁	—	2	128	no	—
61	#41×C₆₁	—	2	144	no	—
62	#41×C₆₁	C₂×D₄	1	48	yes	—
63	#41×C₆₁	C₂⁴	1	16	yes	—
64	#41×C₆₁	C₂⁴	1	96	yes	complemented
65	C₂×Q₈×C₆₁	—	2	6	no	—
66	C₂×Q₈×C₆₁	C₂×D₄	1	12	yes	—
67	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
68	C₂×D₄×C₆₁	—	2	72	no	—
69	C₂×D₄×C₆₁	—	2	384	no	—
70	C₂×D₄×C₆₁	—	2	18	no	—
71	C₂×D₄×C₆₁	—	2	72	no	—
72	C₂×D₄×C₆₁	—	2	144	no	—
73	C₂×D₄×C₆₁	C₂×D₄	1	36	yes	—
74	C₂×D₄×C₆₁	C₂⁴	1	36	yes	—
75	C₂×D₄×C₆₁	C₂⁴	1	96	yes	complemented
76	C₂²×C₄×C₆₁	—	2	2	no	—
77	C₂²×C₄×C₆₁	—	2	72	no	—
78	C₂²×C₄×C₆₁	C₂×D₄	1	18	yes	—
79	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
80	C₂²×C₄×C₆₁	C₂⁴	1	18	yes	—
81	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
82	Q₁₆×C₆₁	C₂⁴	1	16	yes	complemented
83	SD₁₆×C₆₁	C₂⁴	1	96	yes	complemented
84	D₈×C₆₁	C₂⁴	1	48	yes	complemented
85	D₈×C₆₁	C₂⁴	1	96	yes	complemented
86	M₁₆×C₆₁	C₂⁴	1	48	yes	complemented
87	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
88	C₂×C₈×C₆₁	C₂⁴	1	18	yes	—
89	C₂×C₈×C₆₁	C₂⁴	1	48	yes	complemented
90	C₂³×C₆₁	—	2	12	no	—
91	C₂³×C₆₁	—	2	36	no	—
92	C₂³×C₆₁	—	2	96	no	—
93	C₂³×C₆₁	—	4	24	no	—
94	C₂³×C₆₁	—	8	144	no	—
95	C₂³×C₆₁	C₂²×D₄	1	18	yes	—
96	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
97	Q₈×C₆₁	—	2	12	no	—
98	Q₈×C₆₁	C₂²×D₄	1	16	yes	—
99	Q₈×C₆₁	C₂⁵	1	8	yes	—
100	D₄×C₆₁	—	2	96	no	—
101	D₄×C₆₁	—	2	36	no	—
102	D₄×C₆₁	—	2	96	no	—
103	D₄×C₆₁	C₂²×D₄	1	48	yes	—
104	D₄×C₆₁	C₂⁵	1	24	yes	—
105	C₂×C₄×C₆₁	—	2	12	no	—
106	C₂×C₄×C₆₁	—	2	96	no	—
107	C₂×C₄×C₆₁	C₂²×D₄	1	18	yes	—
108	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
109	C₂×C₄×C₆₁	C₂²×D₄	1	36	yes	—
110	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
111	C₂×C₄×C₆₁	C₂⁵	1	12	yes	—
112	C₈×C₆₁	C₂⁵	1	4	yes	—
113	C₈×C₆₁	C₂⁵	1	12	yes	—
114	C₂²×#576	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂²×C₆₁	—	2	36	no	—
116	C₂²×C₆₁	—	2	24	no	—
117	C₂²×C₆₁	—	4	72	no	—
118	C₂²×C₆₁	—	8	96	no	—
119	C₂²×C₆₁	#576	1	4	yes	direct product factor
120	C₂²×C₆₁	C₂³×D₄	1	12	yes	—
121	C₂²×C₆₁	C₂³×D₄	1	3	yes	—
122	C₄×C₆₁	—	2	8	no	—
123	C₄×C₆₁	C₂³×D₄	1	12	yes	—
124	C₄×C₆₁	C₂³×D₄	1	3	yes	—
125	C₄×C₆₁	C₂⁶	1	1	yes	characteristic
126	C₂²×H(5,𝔽₂)	C₂×C₆₁	1	2	yes	complemented
127	C₂×#576	C₂×C₆₁	1	48	yes	direct product factor
128	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	6	yes	complemented
129	C₂²×#135	C₂×C₆₁	1	3	yes	complemented
130	C₂³×D₈	C₂×C₆₁	1	3	yes	complemented
131	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic, complemented
132	C₂×C₆₁	—	2	12	no	—
133	C₂×C₆₁	—	4	24	no	—
134	C₂×C₆₁	C₂×#576	1	6	yes	direct product factor
135	C₂×C₆₁	C₂⁴×D₄	1	1	yes	characteristic
136	C₂×H(5,𝔽₂)	—	2	24	no	—
137	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	48	yes	complemented
138	C₂²×#41	—	2	2	no	—
139	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
140	C₂²×#41	C₂²×C₆₁	1	6	yes	complemented
141	C₂³×D₄	—	2	6	no	—
142	C₂³×D₄	C₂²×C₆₁	1	6	yes	complemented
143	#576	C₂²×C₆₁	1	256	yes	direct product factor
144	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	144	yes	complemented
145	C₂×#135	C₂²×C₆₁	1	72	yes	complemented
146	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
147	C₂²×SD₁₆	C₂²×C₆₁	1	6	yes	complemented
148	C₂²×D₈	C₂²×C₆₁	1	3	yes	complemented
149	C₂²×D₈	C₂²×C₆₁	1	6	yes	complemented
150	C₂²×D₈	C₂²×C₆₁	1	72	yes	complemented
151	C₂×#131	C₂²×C₆₁	1	24	yes	complemented
152	C₂²×M₁₆	C₂²×C₆₁	1	3	yes	complemented
153	C₂³×C₈	C₂²×C₆₁	1	3	yes	complemented
154	C₆₁	C₂²×#576	1	1	yes	characteristic, direct product factor, Sylow
155	C₂⁵	—	2	6	no	—
156	H(5,𝔽₂)	—	2	192	no	—
157	H(5,𝔽₂)	C₂³×C₆₁	1	128	yes	complemented
158	C₂×#41	—	2	48	no	—
159	C₂×#41	—	2	36	no	—
160	C₂×#41	D₄×C₆₁	1	12	yes	—
161	C₂×#41	C₂³×C₆₁	1	12	yes	—
162	C₂×#41	C₂³×C₆₁	1	72	yes	complemented
163	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
164	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
165	C₂²×D₄	—	2	6	no	—
166	C₂²×D₄	—	2	144	no	—
167	C₂²×D₄	—	2	6	no	—
168	C₂²×D₄	—	2	36	no	—
169	C₂²×D₄	D₄×C₆₁	1	3	yes	—
170	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
171	C₂²×D₄	C₂³×C₆₁	1	72	yes	complemented
172	C₂³×C₄	—	2	6	no	—
173	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
174	AGL(1,ℤ/8)	C₂³×C₆₁	1	384	yes	complemented
175	#135	C₂³×C₆₁	1	192	yes	complemented
176	C₂×Q₁₆	C₂³×C₆₁	1	12	yes	complemented
177	C₂×SD₁₆	C₂³×C₆₁	1	72	yes	complemented
178	C₂×D₈	C₂³×C₆₁	1	36	yes	complemented
179	C₂×D₈	C₂³×C₆₁	1	72	yes	complemented
180	C₂×D₈	C₂³×C₆₁	1	192	yes	complemented
181	#131	C₂³×C₆₁	1	64	yes	complemented
182	C₂×M₁₆	C₂³×C₆₁	1	36	yes	complemented
183	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
184	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
185	C₂²×C₈	C₂³×C₆₁	1	36	yes	complemented
186	C₂⁴	—	2	6	no	—
187	C₂⁴	—	2	72	no	—
188	C₂⁴	—	8	24	no	—
189	C₂⁴	C₂×D₄×C₆₁	1	3	yes	—
190	#41	—	2	128	no	—
191	#41	—	2	144	no	—
192	#41	C₂×D₄×C₆₁	1	48	yes	—
193	#41	C₂⁴×C₆₁	1	16	yes	—
194	#41	C₂⁴×C₆₁	1	96	yes	complemented
195	C₂×Q₈	—	2	6	no	—
196	C₂×Q₈	C₂×D₄×C₆₁	1	12	yes	—
197	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
198	C₂×D₄	—	2	72	no	—
199	C₂×D₄	—	2	384	no	—
200	C₂×D₄	—	2	18	no	—
201	C₂×D₄	—	2	72	no	—
202	C₂×D₄	—	2	144	no	—
203	C₂×D₄	C₂×D₄×C₆₁	1	36	yes	—
204	C₂×D₄	C₂⁴×C₆₁	1	36	yes	—
205	C₂×D₄	C₂⁴×C₆₁	1	96	yes	complemented
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	72	no	—
208	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
209	C₂²×C₄	C₂×D₄×C₆₁	1	18	yes	—
210	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
211	C₂²×C₄	C₂⁴×C₆₁	1	18	yes	—
212	Q₁₆	C₂⁴×C₆₁	1	16	yes	complemented
213	SD₁₆	C₂⁴×C₆₁	1	96	yes	complemented
214	D₈	C₂⁴×C₆₁	1	48	yes	complemented
215	D₈	C₂⁴×C₆₁	1	96	yes	complemented
216	M₁₆	C₂⁴×C₆₁	1	48	yes	complemented
217	C₂×C₈	C₂⁴×C₆₁	1	6	yes	—
218	C₂×C₈	C₂⁴×C₆₁	1	18	yes	—
219	C₂×C₈	C₂⁴×C₆₁	1	48	yes	complemented
220	C₂³	—	2	12	no	—
221	C₂³	—	2	36	no	—
222	C₂³	—	2	96	no	—
223	C₂³	—	4	24	no	—
224	C₂³	—	8	144	no	—
225	C₂³	C₂²×D₄×C₆₁	1	18	yes	—
226	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
227	Q₈	—	2	12	no	—
228	Q₈	C₂²×D₄×C₆₁	1	16	yes	—
229	Q₈	C₂⁵×C₆₁	1	8	yes	—
230	D₄	—	2	96	no	—
231	D₄	—	2	36	no	—
232	D₄	—	2	96	no	—
233	D₄	C₂²×D₄×C₆₁	1	48	yes	—
234	D₄	C₂⁵×C₆₁	1	24	yes	—
235	C₂×C₄	—	2	12	no	—
236	C₂×C₄	—	2	96	no	—
237	C₂×C₄	C₂²×D₄×C₆₁	1	18	yes	—
238	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
239	C₂×C₄	C₂²×D₄×C₆₁	1	36	yes	—
240	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
241	C₂×C₄	C₂⁵×C₆₁	1	12	yes	—
242	C₈	C₂⁵×C₆₁	1	4	yes	—
243	C₈	C₂⁵×C₆₁	1	12	yes	—
244	C₂²	—	2	36	no	—
245	C₂²	—	2	24	no	—
246	C₂²	—	4	72	no	—
247	C₂²	—	8	96	no	—
248	C₂²	C₆₁×#576	1	4	yes	direct product factor
249	C₂²	C₂³×D₄×C₆₁	1	12	yes	—
250	C₂²	C₂³×D₄×C₆₁	1	3	yes	—
251	C₄	—	2	8	no	—
252	C₄	C₂³×D₄×C₆₁	1	12	yes	—
253	C₄	C₂³×D₄×C₆₁	1	3	yes	—
254	C₄	C₂⁶×C₆₁	1	1	yes	characteristic
255	C₂	—	2	12	no	—
256	C₂	—	4	24	no	—
257	C₂	C₂×C₆₁×#576	1	6	yes	direct product factor
258	C₂	C₂⁴×D₄×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₆₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₁	C₂	semidirect
2. C₂×C₆₁×#576	C₂	direct (N × H)
3. C₂²×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
4. C₂²×#135×C₆₁	C₂	semidirect
5. C₂³×D₈×C₆₁	C₂	semidirect
6. C₂²×#131×C₆₁	C₂	semidirect
8. C₂×H(5,𝔽₂)×C₆₁	C₂²	semidirect
11. C₂²×#41×C₆₁	C₂²	semidirect
13. C₂³×D₄×C₆₁	C₂²	semidirect
14. C₆₁×#576	C₂²	direct (N × H)
15. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
16. C₂×#135×C₆₁	C₂²	semidirect
17. C₂²×Q₁₆×C₆₁	C₂²	semidirect
18. C₂²×SD₁₆×C₆₁	C₂²	semidirect
19. C₂²×D₈×C₆₁	C₂²	semidirect
20. C₂²×D₈×C₆₁	C₂²	semidirect
21. C₂²×D₈×C₆₁	C₂²	semidirect
22. C₂×#131×C₆₁	C₂²	semidirect
23. C₂²×M₁₆×C₆₁	C₂²	semidirect
24. C₂³×C₈×C₆₁	C₂²	semidirect
27. H(5,𝔽₂)×C₆₁	C₂³	semidirect
32. C₂×#41×C₆₁	C₂³	semidirect
41. C₂²×D₄×C₆₁	C₂³	semidirect
44. AGL(1,ℤ/8)×C₆₁	C₂³	semidirect
45. #135×C₆₁	C₂³	semidirect
46. C₂×Q₁₆×C₆₁	C₂³	semidirect
47. C₂×SD₁₆×C₆₁	C₂³	semidirect
48. C₂×D₈×C₆₁	C₂³	semidirect
49. C₂×D₈×C₆₁	C₂³	semidirect
50. C₂×D₈×C₆₁	C₂³	semidirect
51. #131×C₆₁	C₂³	semidirect
52. C₂×M₁₆×C₆₁	C₂³	semidirect
55. C₂²×C₈×C₆₁	C₂³	semidirect
64. #41×C₆₁	C₂⁴	semidirect
75. C₂×D₄×C₆₁	C₂⁴	semidirect
82. Q₁₆×C₆₁	C₂⁴	semidirect
83. SD₁₆×C₆₁	C₂⁴	semidirect
84. D₈×C₆₁	C₂⁴	semidirect
85. D₈×C₆₁	C₂⁴	semidirect
86. M₁₆×C₆₁	C₂⁴	semidirect
89. C₂×C₈×C₆₁	C₂⁴	semidirect
114. C₂²×#576	C₆₁	direct (N × H)
119. C₂²×C₆₁	#576	direct (N × H)
126. C₂²×H(5,𝔽₂)	C₂×C₆₁	semidirect
127. C₂×#576	C₂×C₆₁	direct (N × H)
128. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
129. C₂²×#135	C₂×C₆₁	semidirect
130. C₂³×D₈	C₂×C₆₁	semidirect
131. C₂²×#131	C₂×C₆₁	semidirect
134. C₂×C₆₁	C₂×#576	direct (N × H)
137. C₂×H(5,𝔽₂)	C₂²×C₆₁	semidirect
140. C₂²×#41	C₂²×C₆₁	semidirect
142. C₂³×D₄	C₂²×C₆₁	semidirect
143. #576	C₂²×C₆₁	direct (N × H)
144. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
145. C₂×#135	C₂²×C₆₁	semidirect
146. C₂²×Q₁₆	C₂²×C₆₁	semidirect
147. C₂²×SD₁₆	C₂²×C₆₁	semidirect
148. C₂²×D₈	C₂²×C₆₁	semidirect
149. C₂²×D₈	C₂²×C₆₁	semidirect
150. C₂²×D₈	C₂²×C₆₁	semidirect
151. C₂×#131	C₂²×C₆₁	semidirect
152. C₂²×M₁₆	C₂²×C₆₁	semidirect
153. C₂³×C₈	C₂²×C₆₁	semidirect
154. C₆₁	C₂²×#576	direct (N × H)
157. H(5,𝔽₂)	C₂³×C₆₁	semidirect
162. C₂×#41	C₂³×C₆₁	semidirect
171. C₂²×D₄	C₂³×C₆₁	semidirect
174. AGL(1,ℤ/8)	C₂³×C₆₁	semidirect
175. #135	C₂³×C₆₁	semidirect
176. C₂×Q₁₆	C₂³×C₆₁	semidirect
177. C₂×SD₁₆	C₂³×C₆₁	semidirect
178. C₂×D₈	C₂³×C₆₁	semidirect
179. C₂×D₈	C₂³×C₆₁	semidirect
180. C₂×D₈	C₂³×C₆₁	semidirect
181. #131	C₂³×C₆₁	semidirect
182. C₂×M₁₆	C₂³×C₆₁	semidirect
185. C₂²×C₈	C₂³×C₆₁	semidirect
194. #41	C₂⁴×C₆₁	semidirect
205. C₂×D₄	C₂⁴×C₆₁	semidirect
212. Q₁₆	C₂⁴×C₆₁	semidirect
213. SD₁₆	C₂⁴×C₆₁	semidirect
214. D₈	C₂⁴×C₆₁	semidirect
215. D₈	C₂⁴×C₆₁	semidirect
216. M₁₆	C₂⁴×C₆₁	semidirect
219. C₂×C₈	C₂⁴×C₆₁	semidirect
248. C₂²	C₆₁×#576	direct (N × H)
257. C₂	C₂×C₆₁×#576	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×H(5,𝔽₂)×C₆₁	2
C₂×C₆₁×#576	2
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₂²×#135×C₆₁	2
C₂³×D₈×C₆₁	2
C₂²×#131×C₆₁	2
C₂²×#576	61

Subgroups — C22×C61×#576 #29566517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₆₁×#576 #29566517